Lion and Snow Leopard- The easiest way is to go to the Apple logo in the Menubar and click About This Mac > More Info> System Report or go to Apple logo in the Menubar and hold down the option key, the "About This Mac" item will change to "System Information" and you can click it. Either way should get you to the System Info screen:MacBook-1.jpg74.18KB80 downloadsClick on Software as seen in the left column as seen in the picture above. It will say "Yes" if running 64-bit and "No" if running 32-bit. This image is taken from a early 2008 MacBook which is not capable of running 64-bit kernel, or Mountain Lion for that matter.

Can This be Changed?

Lion and Snow Leopard are capable of running either 32-bit or 64-bit kernel, not to be confused with 32/64-bit kernel extensions, where 64-bit extensions can run on a 32-bit kernel, but 32-bit extensions will not run on a 64-bit kernel. So to run 64-bit, all your extensions loaded need to be 64-bit capable.

There may be cases where you need to specify if you wan't one or the other to load, usually due to hardware or other compatibility reasons. To do this on a temporary basis, at the Chameleon boot promt type:

for 32-bit

arch=i386

or for 64-bit

arch=x86_64

To make the change more permanent, open the org.chameleon.Boot.plist in your /Extra folder and add either of the above (only one, not both) into the string after kernel flags like this